11L 2s (3/1-equivalent): Difference between revisions

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m Modes intervals
 
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Having 11 large steps and 2 small steps, this MOS family is the first which is true Arcturus scale. However, it still has slightly smeary intonation regarding the generator (or seventh), This smearing causes 3g to be so flat that it tritave reduces into the syntonic continuum.
{{Infobox MOS}}
{{MOS intro}}
Having 11 large steps and 2 small steps, this MOS family is the first which is true Arcturus scale. However, it still has slightly smeary intonation regarding the generator (or major sixth), This smearing causes 3g to be so flat that it tritave reduces into the syntonic continuum of fifths, thus making these scales ridden with pseudo-octaves and pseudo-fifths.


== Modes ==
{{MOS modes}}
== Intervals ==
{{MOS intervals}}
== Scale tree ==
{| class="wikitable"
{| class="wikitable"
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|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 864.525
| style="text-align:center;" | 864.525
590.909
| style="text-align:center;" | 172.905
| style="text-align:center;" | 172.905
118.182
| style="text-align:center;" | 0.00
| style="text-align:center;" | 0.00
| style="text-align:center;" | 691.62
| style="text-align:center;" | 691.62
472.727
| style="text-align:center;" | L=1 s=0
| style="text-align:center;" | L=1 s=0
|-
|-
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| style="text-align:center;" | 36\79
| style="text-align:center;" | 36\79
| style="text-align:center;" | 866.714
| style="text-align:center;" | 866.714
592.405
| style="text-align:center;" | 168.528
| style="text-align:center;" | 168.528
115.19
| style="text-align:center;" | 24.075
| style="text-align:center;" | 24.075
16.456
| style="text-align:center;" | 698.186
| style="text-align:center;" | 698.186
477.215
| style="text-align:center;" | L=7 s=1
| style="text-align:center;" | L=7 s=1
|-
|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 867.068
| style="text-align:center;" | 867.068
592.647
| style="text-align:center;" | 167.82
| style="text-align:center;" | 167.82
114.706
| style="text-align:center;" | 27.969
| style="text-align:center;" | 27.969
19.118
| style="text-align:center;" | 699.248
| style="text-align:center;" | 699.248
477.941
| style="text-align:center;" | L=6 s=1
| style="text-align:center;" | L=6 s=1
|-
|-
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| style="text-align:center;" | 57\125
| style="text-align:center;" | 57\125
| style="text-align:center;" | 867.2915
| style="text-align:center;" | 867.2915
592.8
| style="text-align:center;" | 167.372
| style="text-align:center;" | 167.372
114.4
| style="text-align:center;" | 30.431
| style="text-align:center;" | 30.431
20.8
| style="text-align:center;" | 699.919
| style="text-align:center;" | 699.919
478.4
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 867.558
| style="text-align:center;" | 867.558
592.9825
| style="text-align:center;" | 166.838
| style="text-align:center;" | 166.838
114.035
| style="text-align:center;" | 33.368
| style="text-align:center;" | 33.368
22.807
| style="text-align:center;" | 700.72
| style="text-align:center;" | 700.72
478.947
| style="text-align:center;" | L=5 s=1
| style="text-align:center;" | L=5 s=1
|-
|-
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| style="text-align:center;" | 73\160
| style="text-align:center;" | 73\160
| style="text-align:center;" | 867.767
| style="text-align:center;" | 867.767
593.125
| style="text-align:center;" | 166.421
| style="text-align:center;" | 166.421
113.75
| style="text-align:center;" | 35.662
| style="text-align:center;" | 35.662
24.375
| style="text-align:center;" | 701.346
| style="text-align:center;" | 701.346
479.375
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 867.882
| style="text-align:center;" | 867.882
593.204
| style="text-align:center;" | 166.19
| style="text-align:center;" | 166.19
113.592
| style="text-align:center;" | 36.931
| style="text-align:center;" | 36.931
25.243
| style="text-align:center;" | 701.692
| style="text-align:center;" | 701.692
479.612
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| style="text-align:center;" | 68\149
| style="text-align:center;" | 68\149
| style="text-align:center;" | 868.006
| style="text-align:center;" | 868.006
593.289
| style="text-align:center;" | 165.942
| style="text-align:center;" | 165.942
113.423
| style="text-align:center;" | 38.294
| style="text-align:center;" | 38.294
26.1745
| style="text-align:center;" | 702.064
| style="text-align:center;" | 702.064
479.866
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 868.284
| style="text-align:center;" | 868.284
593.478
| style="text-align:center;" | 165.387
| style="text-align:center;" | 165.387
113.0435.
| style="text-align:center;" | 41.347
| style="text-align:center;" | 41.347
28.261
| style="text-align:center;" | 702.896
| style="text-align:center;" | 702.896
480.445
| style="text-align:center;" | L=4 s=1
| style="text-align:center;" | L=4 s=1
|-
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| style="text-align:center;" | 79\173
| style="text-align:center;" | 79\173
| style="text-align:center;" | 868.523
| style="text-align:center;" | 868.523
593.642
| style="text-align:center;" | 164.909
| style="text-align:center;" | 164.909
112.717
| style="text-align:center;" | 43.976
| style="text-align:center;" | 43.976
30.058
| style="text-align:center;" | 703.613
| style="text-align:center;" | 703.613
480.925
| style="text-align:center;" |  
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 868.609
| style="text-align:center;" | 868.609
593.701
| style="text-align:center;" | 164.736
| style="text-align:center;" | 164.736
112.598
| style="text-align:center;" | 44.928
| style="text-align:center;" | 44.928
30.709
| style="text-align:center;" | 703.873
| style="text-align:center;" | 703.873
481.102
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
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| style="text-align:center;" | 95\208
| style="text-align:center;" | 95\208
| style="text-align:center;" | 868.681
| style="text-align:center;" | 868.681
593.75
| style="text-align:center;" | 164.592
| style="text-align:center;" | 164.592
112.5
| style="text-align:center;" | 45.72
| style="text-align:center;" | 45.72
31.25
| style="text-align:center;" | 704.089
| style="text-align:center;" | 704.089
481.25
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 868.794
| style="text-align:center;" | 868.794
593.827
| style="text-align:center;" | 164.3665
| style="text-align:center;" | 164.3665
112.346
| style="text-align:center;" | 46.962
| style="text-align:center;" | 46.962
32.099
| style="text-align:center;" | 704.428
| style="text-align:center;" | 704.428
481.4815
| style="text-align:center;" | L=7 s=2
| style="text-align:center;" | L=7 s=2
|-
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| style="text-align:center;" | 90\197
| style="text-align:center;" | 90\197
| style="text-align:center;" | 868.9135
| style="text-align:center;" | 868.9135
593.909
| style="text-align:center;" | 164.128
| style="text-align:center;" | 164.128
112.183
| style="text-align:center;" | 48.273
| style="text-align:center;" | 48.273
32.995
| style="text-align:center;" | 704.785
| style="text-align:center;" | 704.785
481.726
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 868.997
| style="text-align:center;" | 868.997
593.9655
| style="text-align:center;" | 163.961
| style="text-align:center;" | 163.961
112.069
| style="text-align:center;" | 49.1885
| style="text-align:center;" | 49.1885
33.621
| style="text-align:center;" | 705.035
| style="text-align:center;" | 705.035
481.897
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| style="text-align:center;" | 69\151
| style="text-align:center;" | 69\151
| style="text-align:center;" | 869.105
| style="text-align:center;" | 869.105
594.04
| style="text-align:center;" | 163.744
| style="text-align:center;" | 163.744
111.9205
| style="text-align:center;" | 50.383
| style="text-align:center;" | 50.383
34.437
| style="text-align:center;" | 705.36
| style="text-align:center;" | 705.36
482.119
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 869.465
| style="text-align:center;" | 869.465
594.286
| style="text-align:center;" | 163.025
| style="text-align:center;" | 163.025
111.429
| style="text-align:center;" | 54.342
| style="text-align:center;" | 54.342
37.143
| style="text-align:center;" | 706.44
| style="text-align:center;" | 706.44
482.857
| style="text-align:center;" | L=3 s=1
| style="text-align:center;" | L=3 s=1
|-
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| style="text-align:center;" | 75\164
| style="text-align:center;" | 75\164
| style="text-align:center;" | 869.7965
| style="text-align:center;" | 869.7965
594.512
| style="text-align:center;" | 162.362
| style="text-align:center;" | 162.362
110.976
| style="text-align:center;" | 57.986
| style="text-align:center;" | 57.986
39.634
| style="text-align:center;" | 707.4345
| style="text-align:center;" | 707.4345
483.537
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 869.886
| style="text-align:center;" | 869.886
594.574
| style="text-align:center;" | 162.182
| style="text-align:center;" | 162.182
110.853
| style="text-align:center;" | 58.375
| style="text-align:center;" | 58.375
40.31
| style="text-align:center;" | 707.704
| style="text-align:center;" | 707.704
483.721
| style="text-align:center;" |  
| style="text-align:center;" |  
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| style="text-align:center;" | 102\223
| style="text-align:center;" | 102\223
| style="text-align:center;" | 869.9525
| style="text-align:center;" | 869.9525
594.619
| style="text-align:center;" | 162.05
| style="text-align:center;" | 162.05
110.762
| style="text-align:center;" | 59.703
| style="text-align:center;" | 59.703
40.807
| style="text-align:center;" | 707.9025
| style="text-align:center;" | 707.9025
483.8565
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 870.043
| style="text-align:center;" | 870.043
594.681
| style="text-align:center;" | 161.8685
| style="text-align:center;" | 161.8685
110.638
| style="text-align:center;" | 60.701
| style="text-align:center;" | 60.701
41.489
| style="text-align:center;" | 708.175
| style="text-align:center;" | 708.175
484.043
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| style="text-align:center;" | 113\247
| style="text-align:center;" | 113\247
| style="text-align:center;" | 870.125
| style="text-align:center;" | 870.125
594.737
| style="text-align:center;" | 161.705
| style="text-align:center;" | 161.705
110.526
| style="text-align:center;" | 61.601
| style="text-align:center;" | 61.601
42.105
| style="text-align:center;" | 708.4205
| style="text-align:center;" | 708.4205
484.2105
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 870.1755
| style="text-align:center;" | 870.1755
594.771
| style="text-align:center;" | 161.604
| style="text-align:center;" | 161.604
110.4575
| style="text-align:center;" | 62.155
| style="text-align:center;" | 62.155
42.484
| style="text-align:center;" | 708.5715
| style="text-align:center;" | 708.5715
484.314
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| style="text-align:center;" | 97\212
| style="text-align:center;" | 97\212
| style="text-align:center;" | 870.234
| style="text-align:center;" | 870.234
594.811
| style="text-align:center;" | 161.487
| style="text-align:center;" | 161.487
| style="text-align:center;" | 62.80
110.377
| style="text-align:center;" | 62.8
42.9245
| style="text-align:center;" | 708.747
| style="text-align:center;" | 708.747
484.434
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| style="text-align:center;" |  
|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 870.386
| style="text-align:center;" | 870.386
594.915
| style="text-align:center;" | 161.182
| style="text-align:center;" | 161.182
110.1695
| style="text-align:center;" | 64.473
| style="text-align:center;" | 64.473
44.068
| style="text-align:center;" | 709.204
| style="text-align:center;" | 709.204
484.746
| style="text-align:center;" | L=5 s=2
| style="text-align:center;" | L=5 s=2
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| style="text-align:center;" | 870.547
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595.025
| style="text-align:center;" | 160.862
| style="text-align:center;" | 160.862
109.95
| style="text-align:center;" | 66.237
| style="text-align:center;" | 66.237
45.274
| style="text-align:center;" | 709.685
| style="text-align:center;" | 709.685
485.075
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 870.613
| style="text-align:center;" | 870.613
595.07
| style="text-align:center;" | 160.729
| style="text-align:center;" | 160.729
109.859
| style="text-align:center;" | 66.97
| style="text-align:center;" | 66.97
45.775
| style="text-align:center;" | 709.885
| style="text-align:center;" | 709.885
485.211
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595.111
| style="text-align:center;" | 160.6095
| style="text-align:center;" | 160.6095
109.778
| style="text-align:center;" | 67.625
| style="text-align:center;" | 67.625
46.222
| style="text-align:center;" | 710.063
| style="text-align:center;" | 710.063
485.333
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 870.775
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595.181
| style="text-align:center;" | 160.406
| style="text-align:center;" | 160.406
109.639
| style="text-align:center;" | 68.745
| style="text-align:center;" | 68.745
46.988
| style="text-align:center;" | 710.369
| style="text-align:center;" | 710.369
485.542
| style="text-align:center;" | L=7 s=3
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| style="text-align:center;" | 870.895
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595.263
| style="text-align:center;" | 160.165
| style="text-align:center;" | 160.165
109.747
| style="text-align:center;" | 70.072
| style="text-align:center;" | 70.072
47.895
| style="text-align:center;" | 710.731
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485.7895
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| style="text-align:center;" | 870.989
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595.327
| style="text-align:center;" | 159.9775
| style="text-align:center;" | 159.9775
109.346
| style="text-align:center;" | 71.101
| style="text-align:center;" | 71.101
48.598
| style="text-align:center;" | 711.011
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485.981
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595.42
| style="text-align:center;" | 159.706
| style="text-align:center;" | 159.706
109.16
| style="text-align:center;" | 72.593
| style="text-align:center;" | 72.593
49.618
| style="text-align:center;" | 711.418
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486.2595
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| style="text-align:center;" | 871.729
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595.833
| style="text-align:center;" | 158.496
| style="text-align:center;" | 158.496
108.333
| style="text-align:center;" | 79.248
| style="text-align:center;" | 79.248
54.167
| style="text-align:center;" | 713.233
| style="text-align:center;" | 713.233
487.5
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596.241
| style="text-align:center;" | 157.3045
| style="text-align:center;" | 157.3045
107.519
| style="text-align:center;" | 85.8024
| style="text-align:center;" | 85.8024
58.647
| style="text-align:center;" | 715.021
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488.722
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| style="text-align:center;" | 872.456
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596.33
| style="text-align:center;" | 157.042
| style="text-align:center;" | 157.042
107.339
| style="text-align:center;" | 87.246
| style="text-align:center;" | 87.246
59.633
| style="text-align:center;" | 715.414
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488.991
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596.392
| style="text-align:center;" | 156.862
| style="text-align:center;" | 156.862
107.2165
| style="text-align:center;" | 88.235
| style="text-align:center;" | 88.235
60.309
| style="text-align:center;" | 715.684
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489.175
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| style="text-align:center;" | 872.662
| style="text-align:center;" | 872.662
596.471
| style="text-align:center;" | 156.632
| style="text-align:center;" | 156.632
107.059
| style="text-align:center;" | 89.504
| style="text-align:center;" | 89.504
61.1765
| style="text-align:center;" | 716.03
| style="text-align:center;" | 716.03
489.412
| style="text-align:center;" | L=7 s=4
| style="text-align:center;" | L=7 s=4
|-
|-
Line 499: Line 655:
| style="text-align:center;" | 106\231
| style="text-align:center;" | 106\231
| style="text-align:center;" | 872.759
| style="text-align:center;" | 872.759
596.537
| style="text-align:center;" | 156.438
| style="text-align:center;" | 156.438
106.926
| style="text-align:center;" | 90.569
| style="text-align:center;" | 90.569
61.905
| style="text-align:center;" | 716.321
| style="text-align:center;" | 716.321
489.61
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 512: Line 672:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 872.815
| style="text-align:center;" | 872.815
596.575
| style="text-align:center;" | 156.325
| style="text-align:center;" | 156.325
106.849
| style="text-align:center;" | 91.19
| style="text-align:center;" | 91.19
62.329
| style="text-align:center;" | 716.49
| style="text-align:center;" | 716.49
489.726
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 525: Line 689:
| style="text-align:center;" | 95\207
| style="text-align:center;" | 95\207
| style="text-align:center;" | 872.878
| style="text-align:center;" | 872.878
596.618
| style="text-align:center;" | 156.199
| style="text-align:center;" | 156.199
106.763
| style="text-align:center;" | 91.882
| style="text-align:center;" | 91.882
62.802
| style="text-align:center;" | 716.679
| style="text-align:center;" | 716.679
489.855
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 538: Line 706:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 873.0285
| style="text-align:center;" | 873.0285
596.721
| style="text-align:center;" | 155.898
| style="text-align:center;" | 155.898
106.557
| style="text-align:center;" | 93.539
| style="text-align:center;" | 93.539
63.934
| style="text-align:center;" | 717.131
| style="text-align:center;" | 717.131
490.164
| style="text-align:center;" | L=5 s=3
| style="text-align:center;" | L=5 s=3
|-
|-
Line 551: Line 723:
| style="text-align:center;" | 101\220
| style="text-align:center;" | 101\220
| style="text-align:center;" | 873.17
| style="text-align:center;" | 873.17
596.818
| style="text-align:center;" | 155.6145
| style="text-align:center;" | 155.6145
106.364
| style="text-align:center;" | 95.098
| style="text-align:center;" | 95.098
65
| style="text-align:center;" | 717.556
| style="text-align:center;" | 717.556
490.4545
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 564: Line 740:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 873.225
| style="text-align:center;" | 873.225
596.855
| style="text-align:center;" | 155.506
| style="text-align:center;" | 155.506
106.289
| style="text-align:center;" | 95.696
| style="text-align:center;" | 95.696
65.408
| style="text-align:center;" | 717.719
| style="text-align:center;" | 717.719
490.566
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 577: Line 757:
| style="text-align:center;" | 118\257
| style="text-align:center;" | 118\257
| style="text-align:center;" | 873.271
| style="text-align:center;" | 873.271
596.887
| style="text-align:center;" | 155.413
| style="text-align:center;" | 155.413
106.226
| style="text-align:center;" | 96.208
| style="text-align:center;" | 96.208
65.759
| style="text-align:center;" | 717.8585
| style="text-align:center;" | 717.8585
490.6615
| style="text-align:center;" | Golden Anti-Arcturus is near here
| style="text-align:center;" | Golden Anti-Arcturus is near here
|-
|-
Line 590: Line 774:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 873.347
| style="text-align:center;" | 873.347
596.938
| style="text-align:center;" | 155.262
| style="text-align:center;" | 155.262
106.122
| style="text-align:center;" | 97.0385
| style="text-align:center;" | 97.0385
66.3265
| style="text-align:center;" | 718.085
| style="text-align:center;" | 718.085
490.816
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 603: Line 791:
| style="text-align:center;" | 107\233
| style="text-align:center;" | 107\233
| style="text-align:center;" | 873.43
| style="text-align:center;" | 873.43
596.996
| style="text-align:center;" | 155.095
| style="text-align:center;" | 155.095
106.009
| style="text-align:center;" | 97.955
| style="text-align:center;" | 97.955
66.953
| style="text-align:center;" | 718.335
| style="text-align:center;" | 718.335
490.987
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 616: Line 808:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 873.49
| style="text-align:center;" | 873.49
597.037
| style="text-align:center;" | 154.974
| style="text-align:center;" | 154.974
105.926
| style="text-align:center;" | 98.62
| style="text-align:center;" | 98.62
67.407
| style="text-align:center;" | 718.516
| style="text-align:center;" | 718.516
491.111
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 629: Line 825:
| style="text-align:center;" | 79\172
| style="text-align:center;" | 79\172
| style="text-align:center;" | 873.572
| style="text-align:center;" | 873.572
597.093
| style="text-align:center;" | 154.81
| style="text-align:center;" | 154.81
105.814
| style="text-align:center;" | 99.521
| style="text-align:center;" | 99.521
68.023
| style="text-align:center;" | 718.762
| style="text-align:center;" | 718.762
491.279
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 642: Line 842:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 873.871
| style="text-align:center;" | 873.871
597.297
| style="text-align:center;" | 154.2125
| style="text-align:center;" | 154.2125
105.405
| style="text-align:center;" | 102.808
| style="text-align:center;" | 102.808
70.27
| style="text-align:center;" | 719.659
| style="text-align:center;" | 719.659
491.892
| style="text-align:center;" | L=3 s=2
| style="text-align:center;" | L=3 s=2
|-
|-
Line 655: Line 859:
| style="text-align:center;" | 74\161
| style="text-align:center;" | 74\161
| style="text-align:center;" | 874.1905
| style="text-align:center;" | 874.1905
597.5155
| style="text-align:center;" | 153.574
| style="text-align:center;" | 153.574
104.696
| style="text-align:center;" | 106.32
| style="text-align:center;" | 106.32
72.671
| style="text-align:center;" | 720.6165
| style="text-align:center;" | 720.6165
492.5465
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 668: Line 876:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 874.286
| style="text-align:center;" | 874.286
597.581
| style="text-align:center;" | 153.3835
| style="text-align:center;" | 153.3835
104.839
| style="text-align:center;" | 107.368
| style="text-align:center;" | 107.368
73.387
| style="text-align:center;" | 720.902
| style="text-align:center;" | 720.902
492.742
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 681: Line 893:
| style="text-align:center;" | 97\211
| style="text-align:center;" | 97\211
| style="text-align:center;" | 874.3585
| style="text-align:center;" | 874.3585
597.63
| style="text-align:center;" | 153.238
| style="text-align:center;" | 153.238
104.739
| style="text-align:center;" | 108.168
| style="text-align:center;" | 108.168
73.934
| style="text-align:center;" | 721.12
| style="text-align:center;" | 721.12
492.891
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 694: Line 910:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 874.462
| style="text-align:center;" | 874.462
597.701
| style="text-align:center;" | 153.03
| style="text-align:center;" | 153.03
104.598
| style="text-align:center;" | 109.308
| style="text-align:center;" | 109.308
74.713
| style="text-align:center;" | 721.431
| style="text-align:center;" | 721.431
493.103
| style="text-align:center;" | L=7 s=5
| style="text-align:center;" | L=7 s=5
|-
|-
Line 707: Line 927:
| style="text-align:center;" | 103\224
| style="text-align:center;" | 103\224
| style="text-align:center;" | 874.56
| style="text-align:center;" | 874.56
597.768
| style="text-align:center;" | 152.836
| style="text-align:center;" | 152.836
104.464
| style="text-align:center;" | 110.381
| style="text-align:center;" | 110.381
75.446
| style="text-align:center;" | 721.724
| style="text-align:center;" | 721.724
493.304
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 720: Line 944:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 874.622
| style="text-align:center;" | 874.622
597.81
| style="text-align:center;" | 152.712
| style="text-align:center;" | 152.712
104.38
| style="text-align:center;" | 111.063
| style="text-align:center;" | 111.063
75.912
| style="text-align:center;" | 721.91
| style="text-align:center;" | 721.91
493.431
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 733: Line 961:
| style="text-align:center;" | 86\187
| style="text-align:center;" | 86\187
| style="text-align:center;" | 874.696
| style="text-align:center;" | 874.696
597.861
| style="text-align:center;" | 152.563
| style="text-align:center;" | 152.563
104.278
| style="text-align:center;" | 111.88
| style="text-align:center;" | 111.88
76.471
| style="text-align:center;" | 722.133
| style="text-align:center;" | 722.133
493.583
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 746: Line 978:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 874.899
| style="text-align:center;" | 874.899
598
| style="text-align:center;" | 152.156
| style="text-align:center;" | 152.156
104
| style="text-align:center;" | 114.117
| style="text-align:center;" | 114.117
78
| style="text-align:center;" | 722.743
| style="text-align:center;" | 722.743
494
| style="text-align:center;" | L=4 s=3
| style="text-align:center;" | L=4 s=3
|-
|-
Line 759: Line 995:
| style="text-align:center;" | 75\163
| style="text-align:center;" | 75\163
| style="text-align:center;" | 875.133
| style="text-align:center;" | 875.133
598.1595
| style="text-align:center;" | 151.69
| style="text-align:center;" | 151.69
103.681
| style="text-align:center;" | 116.684
| style="text-align:center;" | 116.684
79.755
| style="text-align:center;" | 723.443
| style="text-align:center;" | 723.443
494.4785
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 772: Line 1,012:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 875.236
| style="text-align:center;" | 875.236
598.23
| style="text-align:center;" | 151.483
| style="text-align:center;" | 151.483
103.54
| style="text-align:center;" | 117.82
| style="text-align:center;" | 117.82
80.531
| style="text-align:center;" | 723.753
| style="text-align:center;" | 723.753
494.69
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 785: Line 1,029:
| style="text-align:center;" | 81\176
| style="text-align:center;" | 81\176
| style="text-align:center;" | 875.332
| style="text-align:center;" | 875.332
598.2955
| style="text-align:center;" | 151.292
| style="text-align:center;" | 151.292
103.409
| style="text-align:center;" | 118.872
| style="text-align:center;" | 118.872
81.25
| style="text-align:center;" | 724.04
| style="text-align:center;" | 724.04
494.886
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 798: Line 1,046:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 875.503
| style="text-align:center;" | 875.503
598.413
| style="text-align:center;" | 150.949
| style="text-align:center;" | 150.949
103.175
| style="text-align:center;" | 120.759
| style="text-align:center;" | 120.759
82.54
| style="text-align:center;" | 724.554
| style="text-align:center;" | 724.554
495.238
| style="text-align:center;" | L=5 s=4
| style="text-align:center;" | L=5 s=4
|-
|-
Line 811: Line 1,063:
| style="text-align:center;" | 64\139
| style="text-align:center;" | 64\139
| style="text-align:center;" | 875.72
| style="text-align:center;" | 875.72
598.561
| style="text-align:center;" | 150.514
| style="text-align:center;" | 150.514
102.878
| style="text-align:center;" | 123.148
| style="text-align:center;" | 123.148
84.173
| style="text-align:center;" | 725.206
| style="text-align:center;" | 725.206
495.6835
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 823: Line 1,079:
| style="text-align:center;" | 35\76
| style="text-align:center;" | 35\76
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 875.90
| style="text-align:center;" | 875.9
598.684
| style="text-align:center;" | 150.124
| style="text-align:center;" | 150.124
102.632
| style="text-align:center;" | 125.129
| style="text-align:center;" | 125.129
85.526
| style="text-align:center;" | 725.746
| style="text-align:center;" | 725.746
496.053
| style="text-align:center;" | L=6 s=5
| style="text-align:center;" | L=6 s=5
|-
|-
Line 837: Line 1,097:
| style="text-align:center;" | 41\89
| style="text-align:center;" | 41\89
| style="text-align:center;" | 876.1815
| style="text-align:center;" | 876.1815
598.876
| style="text-align:center;" | 149.592
| style="text-align:center;" | 149.592
102.247
| style="text-align:center;" | 128.222
| style="text-align:center;" | 128.222
87.64
| style="text-align:center;" | 726.59
| style="text-align:center;" | 726.59
496.629
| style="text-align:center;" | L=7 s=6
| style="text-align:center;" | L=7 s=6
|-
|-
Line 850: Line 1,114:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 877.825
| style="text-align:center;" | 877.825
600
| colspan="2" style="text-align:center;" | 146.304
| colspan="2" style="text-align:center;" | 146.304
100
| style="text-align:center;" | 731.521
| style="text-align:center;" | 731.521
500
| style="text-align:center;" | L=1 s=1
| style="text-align:center;" | L=1 s=1
|}
|}
[[Category:Abstract MOS patterns]]
[[Category:13-tone scales]]
[[Category:Arcturus]]
[[Category:Tritave]]

Latest revision as of 06:58, 15 December 2024

↖ 10L 1s⟨3/1⟩ ↑ 11L 1s⟨3/1⟩ 12L 1s⟨3/1⟩ ↗
← 10L 2s⟨3/1⟩ 11L 2s (3/1-equivalent) 12L 2s⟨3/1⟩ →
↙ 10L 3s⟨3/1⟩ ↓ 11L 3s⟨3/1⟩ 12L 3s⟨3/1⟩ ↘ 
┌╥╥╥╥╥╥┬╥╥╥╥╥┬┐
│║║║║║║│║║║║║││
│││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLsLLLLLs
sLLLLLsLLLLLL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 7\13 to 6\11 (1024.1 ¢ to 1037.4 ¢)
Dark 5\11 to 6\13 (864.5 ¢ to 877.8 ¢)
Related MOS scales
Parent 2L 9s⟨3/1⟩
Sister 2L 11s⟨3/1⟩
Daughters 13L 11s⟨3/1⟩, 11L 13s⟨3/1⟩
Neutralized 9L 4s⟨3/1⟩
2-Flought 24L 2s⟨3/1⟩, 11L 15s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 7\13 (1024.1 ¢)
Supersoft (L:s = 4:3) 27\50 (1027.1 ¢)
Soft (L:s = 3:2) 20\37 (1028.1 ¢)
Semisoft (L:s = 5:3) 33\61 (1028.9 ¢)
Basic (L:s = 2:1) 13\24 (1030.2 ¢)
Semihard (L:s = 5:2) 32\59 (1031.6 ¢)
Hard (L:s = 3:1) 19\35 (1032.5 ¢)
Superhard (L:s = 4:1) 25\46 (1033.7 ¢)
Collapsed (L:s = 1:0) 6\11 (1037.4 ¢)

11L 2s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 11 large steps and 2 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 1024.1 ¢ to 1037.4 ¢, or from 864.5 ¢ to 877.8 ¢. Having 11 large steps and 2 small steps, this MOS family is the first which is true Arcturus scale. However, it still has slightly smeary intonation regarding the generator (or major sixth), This smearing causes 3g to be so flat that it tritave reduces into the syntonic continuum of fifths, thus making these scales ridden with pseudo-octaves and pseudo-fifths.

Modes

Modes of 11L 2s⟨3/1⟩
UDP Cyclic
order		 Step
pattern
12|0 1 LLLLLLsLLLLLs
11|1 8 LLLLLsLLLLLLs
10|2 2 LLLLLsLLLLLsL
9|3 9 LLLLsLLLLLLsL
8|4 3 LLLLsLLLLLsLL
7|5 10 LLLsLLLLLLsLL
6|6 4 LLLsLLLLLsLLL
5|7 11 LLsLLLLLLsLLL
4|8 5 LLsLLLLLsLLLL
3|9 12 LsLLLLLLsLLLL
2|10 6 LsLLLLLsLLLLL
1|11 13 sLLLLLLsLLLLL
0|12 7 sLLLLLsLLLLLL

Intervals

Intervals of 11L 2s⟨3/1⟩
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 146.3 ¢
Major 1-mosstep M1ms L 146.3 ¢ to 172.9 ¢
2-mosstep Minor 2-mosstep m2ms L + s 172.9 ¢ to 292.6 ¢
Major 2-mosstep M2ms 2L 292.6 ¢ to 345.8 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 345.8 ¢ to 438.9 ¢
Major 3-mosstep M3ms 3L 438.9 ¢ to 518.7 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 518.7 ¢ to 585.2 ¢
Major 4-mosstep M4ms 4L 585.2 ¢ to 691.6 ¢
5-mosstep Minor 5-mosstep m5ms 4L + s 691.6 ¢ to 731.5 ¢
Major 5-mosstep M5ms 5L 731.5 ¢ to 864.5 ¢
6-mosstep Perfect 6-mosstep P6ms 5L + s 864.5 ¢ to 877.8 ¢
Augmented 6-mosstep A6ms 6L 877.8 ¢ to 1037.4 ¢
7-mosstep Diminished 7-mosstep d7ms 5L + 2s 864.5 ¢ to 1024.1 ¢
Perfect 7-mosstep P7ms 6L + s 1024.1 ¢ to 1037.4 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 1037.4 ¢ to 1170.4 ¢
Major 8-mosstep M8ms 7L + s 1170.4 ¢ to 1210.3 ¢
9-mosstep Minor 9-mosstep m9ms 7L + 2s 1210.3 ¢ to 1316.7 ¢
Major 9-mosstep M9ms 8L + s 1316.7 ¢ to 1383.2 ¢
10-mosstep Minor 10-mosstep m10ms 8L + 2s 1383.2 ¢ to 1463.0 ¢
Major 10-mosstep M10ms 9L + s 1463.0 ¢ to 1556.1 ¢
11-mosstep Minor 11-mosstep m11ms 9L + 2s 1556.1 ¢ to 1609.3 ¢
Major 11-mosstep M11ms 10L + s 1609.3 ¢ to 1729.1 ¢
12-mosstep Minor 12-mosstep m12ms 10L + 2s 1729.1 ¢ to 1755.7 ¢
Major 12-mosstep M12ms 11L + s 1755.7 ¢ to 1902.0 ¢
13-mosstep Perfect 13-mosstep P13ms 11L + 2s 1902.0 ¢

Scale tree

Generator cents L s 3g Notes
5\11 864.525

590.909

172.905

118.182

0.00 691.62

472.727

L=1 s=0
36\79 866.714

592.405

168.528

115.19

24.075

16.456

698.186

477.215

L=7 s=1
31\68 867.068

592.647

167.82

114.706

27.969

19.118

699.248

477.941

L=6 s=1
57\125 867.2915

592.8

167.372

114.4

30.431

20.8

699.919

478.4

26\57 867.558

592.9825

166.838

114.035

33.368

22.807

700.72

478.947

L=5 s=1
73\160 867.767

593.125

166.421

113.75

35.662

24.375

701.346

479.375

47\103 867.882

593.204

166.19

113.592

36.931

25.243

701.692

479.612

68\149 868.006

593.289

165.942

113.423

38.294

26.1745

702.064

479.866

21\46 868.284

593.478

165.387

113.0435.

41.347

28.261

702.896

480.445

L=4 s=1
79\173 868.523

593.642

164.909

112.717

43.976

30.058

703.613

480.925

58\127 868.609

593.701

164.736

112.598

44.928

30.709

703.873

481.102

95\208 868.681

593.75

164.592

112.5

45.72

31.25

704.089

481.25

37\81 868.794

593.827

164.3665

112.346

46.962

32.099

704.428

481.4815

L=7 s=2
90\197 868.9135

593.909

164.128

112.183

48.273

32.995

704.785

481.726

53\116 868.997

593.9655

163.961

112.069

49.1885

33.621

705.035

481.897

69\151 869.105

594.04

163.744

111.9205

50.383

34.437

705.36

482.119

16\35 869.465

594.286

163.025

111.429

54.342

37.143

706.44

482.857

L=3 s=1
75\164 869.7965

594.512

162.362

110.976

57.986

39.634

707.4345

483.537

59\129 869.886

594.574

162.182

110.853

58.375

40.31

707.704

483.721

102\223 869.9525

594.619

162.05

110.762

59.703

40.807

707.9025

483.8565

43\94 870.043

594.681

161.8685

110.638

60.701

41.489

708.175

484.043

113\247 870.125

594.737

161.705

110.526

61.601

42.105

708.4205

484.2105

70\153 870.1755

594.771

161.604

110.4575

62.155

42.484

708.5715

484.314

97\212 870.234

594.811

161.487

110.377

62.8

42.9245

708.747

484.434

27\59 870.386

594.915

161.182

110.1695

64.473

44.068

709.204

484.746

L=5 s=2
92\201 870.547

595.025

160.862

109.95

66.237

45.274

709.685

485.075

65\142 870.613

595.07

160.729

109.859

66.97

45.775

709.885

485.211

103\225 870.673

595.111

160.6095

109.778

67.625

46.222

710.063

485.333

38\83 870.775

595.181

160.406

109.639

68.745

46.988

710.369

485.542

L=7 s=3
87\190 870.895

595.263

160.165

109.747

70.072

47.895

710.731

485.7895

49\107 870.989

595.327

159.9775

109.346

71.101

48.598

711.011

485.981

60\131 871.124

595.42

159.706

109.16

72.593

49.618

711.418

486.2595

11\24 871.729

595.833

158.496

108.333

79.248

54.167

713.233

487.5

L=2 s=1
61\133 872.325

596.241

157.3045

107.519

85.8024

58.647

715.021

488.722

50\109 872.456

596.33

157.042

107.339

87.246

59.633

715.414

488.991

89\194 872.546

596.392

156.862

107.2165

88.235

60.309

715.684

489.175

39\85 872.662

596.471

156.632

107.059

89.504

61.1765

716.03

489.412

L=7 s=4
106\231 872.759

596.537

156.438

106.926

90.569

61.905

716.321

489.61

67\146 872.815

596.575

156.325

106.849

91.19

62.329

716.49

489.726

95\207 872.878

596.618

156.199

106.763

91.882

62.802

716.679

489.855

28\61 873.0285

596.721

155.898

106.557

93.539

63.934

717.131

490.164

L=5 s=3
101\220 873.17

596.818

155.6145

106.364

95.098

65

717.556

490.4545

73\159 873.225

596.855

155.506

106.289

95.696

65.408

717.719

490.566

118\257 873.271

596.887

155.413

106.226

96.208

65.759

717.8585

490.6615

Golden Anti-Arcturus is near here
45\98 873.347

596.938

155.262

106.122

97.0385

66.3265

718.085

490.816

107\233 873.43

596.996

155.095

106.009

97.955

66.953

718.335

490.987

62\135 873.49

597.037

154.974

105.926

98.62

67.407

718.516

491.111

79\172 873.572

597.093

154.81

105.814

99.521

68.023

718.762

491.279

17\37 873.871

597.297

154.2125

105.405

102.808

70.27

719.659

491.892

L=3 s=2
74\161 874.1905

597.5155

153.574

104.696

106.32

72.671

720.6165

492.5465

57\124 874.286

597.581

153.3835

104.839

107.368

73.387

720.902

492.742

97\211 874.3585

597.63

153.238

104.739

108.168

73.934

721.12

492.891

40\87 874.462

597.701

153.03

104.598

109.308

74.713

721.431

493.103

L=7 s=5
103\224 874.56

597.768

152.836

104.464

110.381

75.446

721.724

493.304

63\137 874.622

597.81

152.712

104.38

111.063

75.912

721.91

493.431

86\187 874.696

597.861

152.563

104.278

111.88

76.471

722.133

493.583

23\50 874.899

598

152.156

104

114.117

78

722.743

494

L=4 s=3
75\163 875.133

598.1595

151.69

103.681

116.684

79.755

723.443

494.4785

52\113 875.236

598.23

151.483

103.54

117.82

80.531

723.753

494.69

81\176 875.332

598.2955

151.292

103.409

118.872

81.25

724.04

494.886

29\63 875.503

598.413

150.949

103.175

120.759

82.54

724.554

495.238

L=5 s=4
64\139 875.72

598.561

150.514

102.878

123.148

84.173

725.206

495.6835

35\76 875.9

598.684

150.124

102.632

125.129

85.526

725.746

496.053

L=6 s=5
41\89 876.1815

598.876

149.592

102.247

128.222

87.64

726.59

496.629

L=7 s=6
6\13 877.825

600

146.304

100

731.521

500

L=1 s=1
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